Robot Manipulators, New Achievements part 2 docx

Deformation compensation is achieved by update the target position of position loop based on the measured process force and robot stiffness model, while robot feed speed is adjusted to m

while the real-time deformation compensation improves the quality and accuracy The focus

of these two sections will be the implementation of advanced control strategies and further

analysis of robot stiffness modelling, as the preliminary research outcomes for CMRR and

deformation compensation have been already introduced in (Wang, Zhang, & Pan, 2007)

Experimental results are presented at the end of these sections A summary and discussion

is provided in section six

2 Force Control Platform

The active force control platform is the foundation of the strategies adopted to address

various difficulties in robotic machining processes It is implemented on the most recent

ABB IRC5 industrial robot controller which is a general controller for a series of ABB robots

The IRC5 controller includes a flexible teach pedant with a colourful graphic interface and

touch screen which allows user to create customized Human Machine Interface (HMI) very

easily It only takes several minutes for a robot operator to learn the interface for a specific

manufacturing task and it is programming free An ATI 6 DOF force/torque sensor is

equipped on the wrist of the robot to close the outer force loop and realize implicit hybrid

position/force control scheme The system setup for robotic machining with force control is

shown in Fig 1

Fig 1 System setup for robotic machining with force control

The force controller provides two major functions to make the entire programming process

collision free and automatic First function is lead-through, in which robot is compliant in

selected force control directions and stiff in the rest of the position control directions To

change the position or orientation of the robot, the robot operator could simply push or drag

the robot with one hand The second function is called path-learning, in which robot is

compliant in normal to the path direction to make the tool constantly contact with the workpiece Thus, an accurate path could be generated automatically

During the machining process, the force controller provides two more functions to achieve deformation compensation and CMRR In both case, robot is still under position control, that is, stiff at all directions Deformation compensation is achieved by update the target position of position loop based on the measured process force and robot stiffness model, while robot feed speed is adjusted to maintain constant spindle power consumption for CMRR These two strategies are complementary to each other since CMRR adjusts robot speed at feed direction and deformation compensation adjusts the reference target at the rest

of the directions The detailed control strategies for process control of robotic machining will

be explained in section four and five respectively

3 Rapid Robot Programming

Although extensive research efforts have been carried out on the methodologies for programming industry robots, still only two methods are realistic in practical industrial application, which are, on-line programming (jog-and-teach method) and off-line programming (Basanez & Rosell, 2005)(Pires, et al., 2004) On-line programming relies on the experience of robot operators to teach robot motions by jogging the robot to the desired positions using teaching device (usually teach pendent) in real setup Off-line programming generates the robot path from a CAD model of the workpiece in a computer simulated setup The idea of programming by demonstration (PbD) has been proposed long time ago, while requirement of additional hardware devices and complicated calibration process make it unattractive in practical applications The major advantage of the PbD method proposed here is that no additional devices and calibration procedures are required The only sensor implemented for force feedback is an ATI 6 DOF force/torque sensor This simple configuration will minimize the cost and simplify the complexity of the programming process greatly

3.1 Lead-Through

Lead-though is the only step requires human intervention through the entire PbD process The purpose of lead-through is to generate a few gross guiding points, which will be used to calculate the path frame in path-learning as shown in Fig 2 The position accuracy of these guiding points is not critical because these guiding points are not the actual points/targets

in the final program and they will be updated in automatic path-learning However the orientation of these points should be carefully taught since it will determine the path frame and will be kept in the final program

Theatrically all six DOFs could be released under force control and the user can adjust both position and orientation of the robot tool at the same time In practice, we found it is almost impossible to adjust the tool orientation accurately by push/pull with a single hand Thus, a force control jogging mode is created, under which the operator could push/pull the robot tool to any position easily and change the robot tool orientation using the joystick on the teach pendent Since this jogging is under force control, collision is avoided even when the tool is in contact with the workpiece As the instant position and orientation of the robot tool

is displayed on the teach pendant, the operator could make very accurate adjustment on each independent rotation axis

Fig 2 Lead-through and path learning

3.2 Automatic Path-Learning

A robot program based on gross guiding points taught in lead-through is then generated

This program path, consisted of a group of linear movements from one guiding point to the

next, is far different from the actual workpiece contour The tool fixture would either move

into the part or too far away from it

During the automatic path-learning, the robot controller is engaged in a compliant motion

mode, such that only in direction Yp, (Fig 2.) which is perpendicular to path direction Xp,

robot motion is under force control, while all other directions and orientations are still under

position control Further, it can be specified in the controller that a constant contact force in

Yp direction (e.g., 20 N) is maintained Because of this constrain, if the program path is into

in the actual workpiece contour, the tool tip will yield along the Y axis until it reaches the

equilibrium of 20N, resulting a new point which is physically on the workpiece contour On

the other hand, if the program path is away from the workpiece, the controller would bring

the tool tip closer to the workpiece until the equilibrium is reached of 20N

While the robot holding the tool fixture is moving along the workpiece contour, the actual

robot position and orientation are recorded continuously As described above, the tool tip

would always be in continuous contact with the workpiece, resulting a recorded spatial

relationship that is the exact replicate between the tool fixture and the workpiece A robot

program generated based on recorded path can be directly used to carry out the actual

process

3.3 Post Processing

After tracking the workpiece contour, the data from logging the robot position have to be

filtered and reduced to generate a robot program The measurements around sharp corners

are often influenced by noise due to high dynamic forces, which has influence on the contact

force By using a threshold for the maximum and minimum acceptable contact force, the

measurements influenced by this type of noise are removed This is called force threshold

filtering

The amount of the targets from automatic path-learning are disproportionately large since the robot controller can recorded the points as fast as every 4 ms An approach, namely deviation height method, is used to approximating the contour by straight-line segments

As shown in Fig 3, a straight line is made from a certain starting point on the contour to the current point The deviation height is calculated between the line and each of the intermediate points The deviation height is the length of the normal vector between the point and the line The current point is displaced along the contour until the deviation height exceeds a certain limit The previous point is then used as starting point for the next line segment This continues until the whole contour is approximated with straight-line segments From the reduced data, a robot program is generated in a standard format The user could specify tool definitions, desired path velocity and orientation of the tool

Fig 3 Deviation height method

3.4 Experimental Results for PbD

With force control integrated in IRC5 controller, PbD method is available for a group of ABB industrial manipulators An automatic deburring system using IRB 4400 manipulator is designed to clean the groove of a water pump to guarantee a seamless interface between two pump surfaces, as shown in Fig 4

A 2 mm cutting tool, driven by ultra high speed (~18,000rpm) air spindle is adopted to achieve this task Since the groove is only about 5 mm wide and has contoured 2D shape, manually teaching a high quality program to clean the complete groove is almost impossible Due to the process requirement, the cutting tool is always perpendicular to the surface of water pump During path-learning, a contact force normal to the edge of 10 N is used, while the robot path learning velocity is set at 5mm/s As shown in Fig 5, the curvature of recorded targets changes dramatically along the path The blue points represent the targets in the final cutting program, while the read points represent the offset targets in the test program The average robot feed speed during the cutting process is about

10 mm/s, while the exact feed speed is determined by the local curvature, which is slower at sharp corner, to ensure a smooth motion throughout the path The point reduction technique is performed on the filtered measurements A deviation height of 0.2mm reduced the thousands of points recorded by the robot controller every 4 ms to about 300 points

Fig 2 Lead-through and path learning

3.2 Automatic Path-Learning

A robot program based on gross guiding points taught in lead-through is then generated

This program path, consisted of a group of linear movements from one guiding point to the

next, is far different from the actual workpiece contour The tool fixture would either move

into the part or too far away from it

During the automatic path-learning, the robot controller is engaged in a compliant motion

mode, such that only in direction Yp, (Fig 2.) which is perpendicular to path direction Xp,

robot motion is under force control, while all other directions and orientations are still under

position control Further, it can be specified in the controller that a constant contact force in

Yp direction (e.g., 20 N) is maintained Because of this constrain, if the program path is into

in the actual workpiece contour, the tool tip will yield along the Y axis until it reaches the

equilibrium of 20N, resulting a new point which is physically on the workpiece contour On

the other hand, if the program path is away from the workpiece, the controller would bring

the tool tip closer to the workpiece until the equilibrium is reached of 20N

While the robot holding the tool fixture is moving along the workpiece contour, the actual

robot position and orientation are recorded continuously As described above, the tool tip

would always be in continuous contact with the workpiece, resulting a recorded spatial

relationship that is the exact replicate between the tool fixture and the workpiece A robot

program generated based on recorded path can be directly used to carry out the actual

process

3.3 Post Processing

After tracking the workpiece contour, the data from logging the robot position have to be

filtered and reduced to generate a robot program The measurements around sharp corners

are often influenced by noise due to high dynamic forces, which has influence on the contact

force By using a threshold for the maximum and minimum acceptable contact force, the

measurements influenced by this type of noise are removed This is called force threshold

filtering

The amount of the targets from automatic path-learning are disproportionately large since the robot controller can recorded the points as fast as every 4 ms An approach, namely deviation height method, is used to approximating the contour by straight-line segments

As shown in Fig 3, a straight line is made from a certain starting point on the contour to the current point The deviation height is calculated between the line and each of the intermediate points The deviation height is the length of the normal vector between the point and the line The current point is displaced along the contour until the deviation height exceeds a certain limit The previous point is then used as starting point for the next line segment This continues until the whole contour is approximated with straight-line segments From the reduced data, a robot program is generated in a standard format The user could specify tool definitions, desired path velocity and orientation of the tool

Fig 3 Deviation height method

3.4 Experimental Results for PbD

With force control integrated in IRC5 controller, PbD method is available for a group of ABB industrial manipulators An automatic deburring system using IRB 4400 manipulator is designed to clean the groove of a water pump to guarantee a seamless interface between two pump surfaces, as shown in Fig 4

A 2 mm cutting tool, driven by ultra high speed (~18,000rpm) air spindle is adopted to achieve this task Since the groove is only about 5 mm wide and has contoured 2D shape, manually teaching a high quality program to clean the complete groove is almost impossible Due to the process requirement, the cutting tool is always perpendicular to the surface of water pump During path-learning, a contact force normal to the edge of 10 N is used, while the robot path learning velocity is set at 5mm/s As shown in Fig 5, the curvature of recorded targets changes dramatically along the path The blue points represent the targets in the final cutting program, while the read points represent the offset targets in the test program The average robot feed speed during the cutting process is about

10 mm/s, while the exact feed speed is determined by the local curvature, which is slower at sharp corner, to ensure a smooth motion throughout the path The point reduction technique is performed on the filtered measurements A deviation height of 0.2mm reduced the thousands of points recorded by the robot controller every 4 ms to about 300 points

Fig 4 Experimental setup for PbD

Fig 5 Results from path-learning

With this programming strategy, generating a program for a water pump with complex

contour, including more than three hundred robot target points, could be completed within

one hour instead of several weeks by an experienced robot programmer During this

programming procedure, the operator is only involved with the first step of teaching the

gross movement of the robot, while the bulk of the procedure is automated by the robot

controller

4 Controlled Material Removal Rate

The MRR in machining process is usually controlled by adjusting the tool feedrate In robotic machining process, this means regulating robot feed speed to maintain a constant MRR Machining force and spindle power are two variables proportional to MRR, which could be used to control robot feed speed With 6-DOF force sensor fixed on robot wrist, the cutting force is available on real-time Most spindles have an analog output whose value is proportional to the spindle current With force feed back or spindle current feed back, MRR could be regulated to avoid tool damage and spindle stall

In most cases, the relationship between process force and tool feedrate is nonlinear, and the process parameters, which describe the nonlinear relationship, are constantly changing due

to the variations of the cutting conditions, such as, depth-of-cut , width-of-cut, spindle motor speed, and tool wearing condition, etc Most of the time, conservative gains have to

be chosen in order to maintain the stability of the close-loop system, while trading off the control performances

Three different control strategies, PI control, adaptive control and fuzzy control, are designed to satisfy various process requirements PI control is easy to tune and is very reliable Adaptive control provides a more stable solution for machining process Fuzzy control, which provides a much faster response by sacrificing control accuracy, is the best method for applications require fast robot feed speed

Fig 6 Robotic end milling process setup

4.1 Robot Dynamic Model

A robotic milling process using industrial robot is shown in Fig 6 The cutting force of this milling process is regulated by adjusting the tool feedrate Since the tool is mounted on the robot end-effector, the tool feedrate is controlled by commanding robot end-effector speed Thus, the robot dynamic model for this machining process is the dynamics from the command speed to the actual end-effector speed The end-effector speed is controlled by the robot position controller A model is identified via experiments for this position controlled close-loop system, which represents the dynamics from command speed to actual end-effector speed

Fig 4 Experimental setup for PbD

Fig 5 Results from path-learning

With this programming strategy, generating a program for a water pump with complex

contour, including more than three hundred robot target points, could be completed within

one hour instead of several weeks by an experienced robot programmer During this

programming procedure, the operator is only involved with the first step of teaching the

gross movement of the robot, while the bulk of the procedure is automated by the robot

controller

4 Controlled Material Removal Rate

The MRR in machining process is usually controlled by adjusting the tool feedrate In robotic machining process, this means regulating robot feed speed to maintain a constant MRR Machining force and spindle power are two variables proportional to MRR, which could be used to control robot feed speed With 6-DOF force sensor fixed on robot wrist, the cutting force is available on real-time Most spindles have an analog output whose value is proportional to the spindle current With force feed back or spindle current feed back, MRR could be regulated to avoid tool damage and spindle stall

In most cases, the relationship between process force and tool feedrate is nonlinear, and the process parameters, which describe the nonlinear relationship, are constantly changing due

to the variations of the cutting conditions, such as, depth-of-cut , width-of-cut, spindle motor speed, and tool wearing condition, etc Most of the time, conservative gains have to

be chosen in order to maintain the stability of the close-loop system, while trading off the control performances

Three different control strategies, PI control, adaptive control and fuzzy control, are designed to satisfy various process requirements PI control is easy to tune and is very reliable Adaptive control provides a more stable solution for machining process Fuzzy control, which provides a much faster response by sacrificing control accuracy, is the best method for applications require fast robot feed speed

Fig 6 Robotic end milling process setup

4.1 Robot Dynamic Model

A robotic milling process using industrial robot is shown in Fig 6 The cutting force of this milling process is regulated by adjusting the tool feedrate Since the tool is mounted on the robot end-effector, the tool feedrate is controlled by commanding robot end-effector speed Thus, the robot dynamic model for this machining process is the dynamics from the command speed to the actual end-effector speed The end-effector speed is controlled by the robot position controller A model is identified via experiments for this position controlled close-loop system, which represents the dynamics from command speed to actual end-effector speed

The dynamic model identified is given as

431300098670

575

433000045800

63)

(

)(

2 3

s

s s

s f

s f

c

(1) Where f(s) is the actual end-effector speed, fc(s) is the commanded end-effector speed

The dynamic model Eq (1) is a stable non-minimum phase system, and its root locus is

shown in Fig 7

Fig 7.Root locus of robot dynamic model

4.2 Process Force Model

MRR is a measurement of how fast material is removed from a workpiece; it can be

calculated by multiplying the cross-sectional area (width of cut times depth of cut) by the

linear feed speed of the tool:

f d w MRR    (2) Where w is width-of-cut (mm), d is depth-of-cut (mm), f is feed speed (mm/s)

Since it is difficult to measure the value of MRR directly, MRR is controlled by regulating

the cutting force, which is readily available in real-time from a 6-DOF force sensor fixed on

the robot wrist The relationship between the machining process force and the tool feed

speed is nonlinear and time-varying, as shown in the following dynamic model (Landers &



w K

K  C (4)

K is considered as a varied process gain Then, the force model is rewritten as a static model:



 f Kd

F  (5) The depth-of-cut, d, depends on the geometry of the workpiece surface It usually changes during the machining process, and is difficult to be measured on-line accurately The cutting depth is the major contributor that causes the process parameter change during the machining process K ,  and depend on those cutting conditions, such as, spindle speed, tool and workpiece material, and tool wearing condition, etc, which are pretty stable during the cutting process If the tool and/or the workpiece are changed, these parameters could change dramatically But they are not changing as quickly as the depth-of-cut d does during the machining process as explained above A force model, which is only valid for the specific tool and workpiece setup in ABB robotics lab is identified from experiments as

5 0 9 0

23d f

F  (6)

Eq (6) models the process force very well from milling experimental data The tool feedrate

f is chosen as the control variable, i.e., to control the process force by adjusting the feed speed

4.3 MRR Control Strategy

In roughing cycles, maximum material removal rates are even more critical than precision and surface finish Conventionally, feed speed is kept constant in spite of variation of depth-of-cut during the pre-machining process of foundry part This will introduce a dramatic change of MRR, which induces a very conservative selection of machining parameters to avoid tool breakage and spindle stall The idea of MRR control is to adjust the feed speed to keep MRR constant during the whole machining process As a result, a much faster feed speed, instead of conservative feed speed based on maximal depth-of-cut position, could be adopted Fig 8 illustrates the idea of MRR control while depth-of-cut changes during milling operation (Pan, 2006)

The dynamic model identified is given as

431300098670

575

433000045800

63)

(

)(

2 3

s

s s

s f

s f

c

(1) Where f(s) is the actual end-effector speed, fc(s) is the commanded end-effector speed

The dynamic model Eq (1) is a stable non-minimum phase system, and its root locus is

shown in Fig 7

Fig 7.Root locus of robot dynamic model

4.2 Process Force Model

MRR is a measurement of how fast material is removed from a workpiece; it can be

calculated by multiplying the cross-sectional area (width of cut times depth of cut) by the

linear feed speed of the tool:

f d

w MRR    (2)

Where w is width-of-cut (mm), d is depth-of-cut (mm), f is feed speed (mm/s)

Since it is difficult to measure the value of MRR directly, MRR is controlled by regulating

the cutting force, which is readily available in real-time from a 6-DOF force sensor fixed on

the robot wrist The relationship between the machining process force and the tool feed

speed is nonlinear and time-varying, as shown in the following dynamic model (Landers &

f d

K F



w K

K  C (4)

K is considered as a varied process gain Then, the force model is rewritten as a static model:



 f Kd

F  (5) The depth-of-cut, d, depends on the geometry of the workpiece surface It usually changes during the machining process, and is difficult to be measured on-line accurately The cutting depth is the major contributor that causes the process parameter change during the machining process K,  and depend on those cutting conditions, such as, spindle speed, tool and workpiece material, and tool wearing condition, etc, which are pretty stable during the cutting process If the tool and/or the workpiece are changed, these parameters could change dramatically But they are not changing as quickly as the depth-of-cut d does during the machining process as explained above A force model, which is only valid for the specific tool and workpiece setup in ABB robotics lab is identified from experiments as

5 0 9 0

23d f

F  (6)

Eq (6) models the process force very well from milling experimental data The tool feedrate

f is chosen as the control variable, i.e., to control the process force by adjusting the feed speed

4.3 MRR Control Strategy

In roughing cycles, maximum material removal rates are even more critical than precision and surface finish Conventionally, feed speed is kept constant in spite of variation of depth-of-cut during the pre-machining process of foundry part This will introduce a dramatic change of MRR, which induces a very conservative selection of machining parameters to avoid tool breakage and spindle stall The idea of MRR control is to adjust the feed speed to keep MRR constant during the whole machining process As a result, a much faster feed speed, instead of conservative feed speed based on maximal depth-of-cut position, could be adopted Fig 8 illustrates the idea of MRR control while depth-of-cut changes during milling operation (Pan, 2006)

Safe &

Conservative Aggressive

Failure and dangerous condition

Optimal

Safe &

Conservative Aggressive

Failure and dangerous condition

Optimal

Fig 8 Controlled material removal rate

Fig 9 The force control loop for CMRR

4.3.1 Force Control Sturcture

The block diagram of CMRR is shown in Fig 9 The cutting force is controlled by varying

the robot end-effecter speed in tool feed direction The difference between the reference

force and the measured cutting force is input to the MRR controller In actual

implementation, the robot motion is planned in advance based on a pre-selected command

speed The output of MRR controller is a term called speed_ratio, which is a ratio (e.g from

0 to 1) of the actual robot feed speed to interpolate the reference trajectory in order to adjust

the tool feedrate Thus the command speed is the greatest speed robot can move If the

measured cutting force is larger than reference force, robot will slow down; otherwise robot

will speed up until it reaches command speed The CMRR function may implement several

control approaches under the indirect force control framework Three different control

strategies, classical control (PI), adaptive control, and fuzzy logic control, will be introduced

F   f (7) Where K f Kd The effects of parametersK, d , and  to the process force are lumped into one parameter, force process gain Kf

Define

 1)

(F

F  (8) Together with Eq (7), we get

kf f K F

F( )1  ( f)1   (9) Where k (K f)1  is time-varying Instead of controlling cutting forceF, we control F

to follow the new command force, i.e., F  r (F r)1 , which is equivalent as controlling F

to follow the original reference force Fr By using Eq (9), the nonlinear system is exactly linearized, and the linear system design technique can be applied to design a controller for the nonlinear system PI type control is selected to achieve null steady-state error The derivative term is not desirable due to the large noise associated with force readings The PI control in is given as

s

K K

015.0



p

K , K i  (11) Where  will be chosen to make the open loop gain of the whole system at the desired value The magnitude of open loop gain, defined as kKp determines the stability of the system Conservative Kp and Ki are selected to ensure system still stable while the force process gain ktakes the maximal value The desired system response is that small overshot for command feed speed

4.3.3 Adaptive Control

Since depth-of-cut and width-of-cut are likely to change dramatically due to the complex shape of workpiece and varied bur size, the force process gain k will vary dramatically during the machining process The fixed-gain PI control will surely have problems to

Safe &

Conservative Aggressive

Failure and dangerous condition

Optimal

Safe &

Conservative Aggressive

Failure and dangerous condition

Optimal

Fig 8 Controlled material removal rate

Fig 9 The force control loop for CMRR

4.3.1 Force Control Sturcture

The block diagram of CMRR is shown in Fig 9 The cutting force is controlled by varying

the robot end-effecter speed in tool feed direction The difference between the reference

force and the measured cutting force is input to the MRR controller In actual

implementation, the robot motion is planned in advance based on a pre-selected command

speed The output of MRR controller is a term called speed_ratio, which is a ratio (e.g from

0 to 1) of the actual robot feed speed to interpolate the reference trajectory in order to adjust

the tool feedrate Thus the command speed is the greatest speed robot can move If the

measured cutting force is larger than reference force, robot will slow down; otherwise robot

will speed up until it reaches command speed The CMRR function may implement several

control approaches under the indirect force control framework Three different control

strategies, classical control (PI), adaptive control, and fuzzy logic control, will be introduced

F   f (7) Where K f Kd The effects of parametersK, d , and  to the process force are lumped into one parameter, force process gain Kf

Define

 1)

(F

F  (8) Together with Eq (7), we get

kf f K F

F( )1  ( f)1   (9) Where k (K f)1  is time-varying Instead of controlling cutting forceF, we control F

to follow the new command force, i.e., F  r (F r)1 , which is equivalent as controlling F

to follow the original reference force Fr By using Eq (9), the nonlinear system is exactly linearized, and the linear system design technique can be applied to design a controller for the nonlinear system PI type control is selected to achieve null steady-state error The derivative term is not desirable due to the large noise associated with force readings The PI control in is given as

s

K K

015.0



p

K , K i  (11) Where  will be chosen to make the open loop gain of the whole system at the desired value The magnitude of open loop gain, defined as kKp determines the stability of the system Conservative Kp and Ki are selected to ensure system still stable while the force process gain ktakes the maximal value The desired system response is that small overshot for command feed speed

4.3.3 Adaptive Control

Since depth-of-cut and width-of-cut are likely to change dramatically due to the complex shape of workpiece and varied bur size, the force process gain k will vary dramatically during the machining process The fixed-gain PI control will surely have problems to

maintain the stability and consistent system performance for wide range of cutting

conditions From Fig 7, the close loop system becomes unstable when the open loop gain is

greater than 1.89, which is consistent with our observations in machining experiments So it

is very important to adjust controller gains to compensate process parameter changes, in

order to maintain close-loop system stability during the machining process

A self-tuning mechanism is proposed here to adaptively adjust the gain of PI controller to

maintain a stable machining process The self-tuning PI controller is shown in Fig 10 There

is low positive speed_ratio output limit (because negative or larger than 1 speed_ratio is

meaningless) assigned for tool feedrate command to avoid “stop and go” situation So

saturation nonlinearity is introduced into the control system The anti-windup scheme is

also necessary for the PI control to avoid the integration windup

Let Vr be the maximum feed speed that the tool can be commanded The saturation

u u

11)( (12) Where   0 and  Vr is the minimum feedrate command for the machining process

Fig 10 Robotic machining system with self-tuning PI control

Without considering the saturation nonlinearity in the system block shown in Fig 10, we set

the open loop gain at 28.84, and the close loop system will have a dominant conjugate pair

of poles with a damping factor around 0.7 The close loop system will have a quick response

and very small overshoot, with the above damping factor From Eq (1), (9), (10), and (11),

the open loop gain of the system is calculated as

84.28





V r k

 (13) Combine Eq (11) and Eq (13), the proportional and integral gains can be given as

k V

K

r

I  28.84ˆ , K V r k

P  0.432ˆ (14) Where kˆ is the on-line estimation of k in Eq (9) Eq (14) is used as the self-tuning rules for the PI controller, which aims to maintain the open loop gain at 28.84

The following standard recursive linear least square (RLS) method is used to identify k and

 of Eq (9)

)()1()(

)()1()

(

t x t P t x

t x t P t

()1()(t  t  k t y t  t x t



)1()]

()([1)(t  IK t x t P t

 (15) Where(t ) (lnk(t) ) ; y(t)lnF(t) ; x( t) (1 ln f(t )T ; t1,2,3, is the sampling point;  is the forgetting factor, which is usually chosen between 0.95 and 0.99 The on-line identified kˆ and ˆ are used in Eq (9) and Eq (14) respectively as the adaptive rules

4.3.4 Fuzzy Logic Control

Although PI control and adaptive control provide stable and zero static error solutions for MRR control, they are only feasible for applications with slow feed speed, such as end milling and grinding Their response is limited by the open loop gain to maintain a stable performance For deburring applications, where the cycle time is critical, faster feed speed

up to 200 mm/s is usually required Also, the variation of material to be removed (bur size)

is more dramatic in deburring process Even with the largest stable gain, the PI and adaptive controller could not response fast enough to prevent spindle stall or robot vibration Derivative term (change of force) must be included in the controller to predict the force trend and achieve faster response Since the force/spindle current signal is very noisy, it is not practical to expand the PI control to a complete PID controller A more intuitive control method must be adopted here to address this problem since the change of force information

is only critical at the moment when the cutting tool start to engage a large bur

Fuzzy control is a very popular approach for performing the task of controller design because it is able to transfer human skills to some linguistic rules Therefore, fuzzy control is often applied to some ill-defined systems or systems without mathematical models In this robotic machining situation we use a Mamdani type fuzzy PD control law to regulate the machining force In Mamdani method, fuzzy logic controller (FLC) is viewed as directly translating external performance specifications and observations of plant behavior into a rule-based linguistic control strategy

A FLC is a control law described by a knowledge base (defined with simple IF THEN type rules over variables vaguely defined fuzzy variables) and an inference mechanism to obtain the current output control value The designed FLC has three inputs, force difference, filtered change of force difference, and previous output speed_ratio, and one output change

of speed_ratio The inputs are divided in levels in accordance with the observed sensor

maintain the stability and consistent system performance for wide range of cutting

conditions From Fig 7, the close loop system becomes unstable when the open loop gain is

greater than 1.89, which is consistent with our observations in machining experiments So it

is very important to adjust controller gains to compensate process parameter changes, in

order to maintain close-loop system stability during the machining process

A self-tuning mechanism is proposed here to adaptively adjust the gain of PI controller to

maintain a stable machining process The self-tuning PI controller is shown in Fig 10 There

is low positive speed_ratio output limit (because negative or larger than 1 speed_ratio is

meaningless) assigned for tool feedrate command to avoid “stop and go” situation So

saturation nonlinearity is introduced into the control system The anti-windup scheme is

also necessary for the PI control to avoid the integration windup

Let Vr be the maximum feed speed that the tool can be commanded The saturation

u u

11

)( (12)

Where   0 and  Vr is the minimum feedrate command for the machining process

Fig 10 Robotic machining system with self-tuning PI control

Without considering the saturation nonlinearity in the system block shown in Fig 10, we set

the open loop gain at 28.84, and the close loop system will have a dominant conjugate pair

of poles with a damping factor around 0.7 The close loop system will have a quick response

and very small overshoot, with the above damping factor From Eq (1), (9), (10), and (11),

the open loop gain of the system is calculated as

84

k V

K

r

I  28.84ˆ , K V r k

P 0.432ˆ (14) Where kˆ is the on-line estimation of k in Eq (9) Eq (14) is used as the self-tuning rules for the PI controller, which aims to maintain the open loop gain at 28.84

The following standard recursive linear least square (RLS) method is used to identify k and

 of Eq (9)

)()1()(

)()1()

(

t x t P t x

t x t P t

()1()(t  t k t y t  t x t



)1()]

()([1)(t  IK t x t P t

 (15) Where(t ) (lnk(t) ) ; y(t)lnF(t) ; x( t) (1 ln f(t )T ; t1,2,3, is the sampling point;  is the forgetting factor, which is usually chosen between 0.95 and 0.99 The on-line identified kˆ and ˆ are used in Eq (9) and Eq (14) respectively as the adaptive rules

4.3.4 Fuzzy Logic Control

Although PI control and adaptive control provide stable and zero static error solutions for MRR control, they are only feasible for applications with slow feed speed, such as end milling and grinding Their response is limited by the open loop gain to maintain a stable performance For deburring applications, where the cycle time is critical, faster feed speed

up to 200 mm/s is usually required Also, the variation of material to be removed (bur size)

is more dramatic in deburring process Even with the largest stable gain, the PI and adaptive controller could not response fast enough to prevent spindle stall or robot vibration Derivative term (change of force) must be included in the controller to predict the force trend and achieve faster response Since the force/spindle current signal is very noisy, it is not practical to expand the PI control to a complete PID controller A more intuitive control method must be adopted here to address this problem since the change of force information

is only critical at the moment when the cutting tool start to engage a large bur

Fuzzy control is a very popular approach for performing the task of controller design because it is able to transfer human skills to some linguistic rules Therefore, fuzzy control is often applied to some ill-defined systems or systems without mathematical models In this robotic machining situation we use a Mamdani type fuzzy PD control law to regulate the machining force In Mamdani method, fuzzy logic controller (FLC) is viewed as directly translating external performance specifications and observations of plant behavior into a rule-based linguistic control strategy

A FLC is a control law described by a knowledge base (defined with simple IF THEN type rules over variables vaguely defined fuzzy variables) and an inference mechanism to obtain the current output control value The designed FLC has three inputs, force difference, filtered change of force difference, and previous output speed_ratio, and one output change

of speed_ratio The inputs are divided in levels in accordance with the observed sensor

characteristics and fuzzyfied using triangular membership functions.(Galichet & Foulloy,

1995) The output is fuzzyfied in the same way The rule base is constructed using a

methodology similar to that in the work of (Li, & Gatland, 1996) The rule base consist three

groups of rules:

1) Force limit rule: Basic rules to speed up or slow down robot based on the

difference of measured force and reference force This group of rules perform

similarly to classical control method

2) Force trend rule: This group of rules are specially implemented to detect the

large burs by evaluate the trend of force difference Proper set of force trend

rule could reduce overshoot of cutting force and achieves fast response

3) System failure protection rule: Used for safety purpose When speed_ratio is

already on lowest stage and process force is still high, robot will stop to avoid

motor overload and robot vibration

FLC generates change of speed_ratio through evaluating various rules Instead of changing

speed_ratio continuously as in classical PID control, speed_ratio is set to several stages The

reason behind this is that continuously adjusting feed speed is not desirable for machining

process because it increase tool wear and deteriorate surface quality Since a too slow feed

speed will change the chip generation mechanism, that is, tool becomes rubbing instead of

cutting the workpiece; the minimal feed speed is also set Although ideally more stages

means more control accuracy, five stages (0.2, 0.4, 0.6 0.8, 1.0) would be enough for most

applications A special case is two-stage switching control which has only low or full speed

Two-stage switching control, which sacrifices control accuracy to achieve faster response, is

a very attractive control method for many deburring process One such example will be

presented in the next session

4.4 Experimental Results for CMRR

Experimental studies are conducted for an end milling process to verify the stability and

performance of the proposed PI control and adaptive control algorithm The robot used in

the milling process is the ABB IRB 6400, the same robot on which we have done the

parameter identification The setup of robotic end milling process is shown as Fig 6

During the end milling experiment, a spindle was hold by the robot arm, and an aluminum

block (AL2040) is fixed on a steel table The cutting depth of the process was changed from 1

mm to 3 mm with a step of 1 mm Both fixed gain PI control algorithm and self-tuning PI

control algorithm, proposed, were tested with the same experimental setup The control

system performance and stability are compared for these two controllers The experiment

results for fixed-gain PI controller and for self-tuning PI controller are shown in Fig 11 and

Fig 12, respectively

The reference force was set at 250 N for the experiments When the cutting depth is 1mm,

both controllers are saturated with a full command speed at 30 mm/s When the cutting

depth changed to 2 mm, the fixed-gain PI controller started to vibrate, but still stable When

the cutting depth changed to 3 mm, the fixed-gain PI controller became unstable, just as

predicted in the simulation results On the other hand, the self-tuning adaptive controller

maintained the stability and performance for all the cutting depths

0100200300

Fig 11 Fixed-gain PI control experiment result

0100200300

to remove the burs The limit of this system is the spindle power, which is equivalent to about 300 N Without the CMRR function, the spindle will stall at the bur location and the entire system setup will be damaged Since the bur location and size are not predicable,

characteristics and fuzzyfied using triangular membership functions.(Galichet & Foulloy,

1995) The output is fuzzyfied in the same way The rule base is constructed using a

methodology similar to that in the work of (Li, & Gatland, 1996) The rule base consist three

groups of rules:

1) Force limit rule: Basic rules to speed up or slow down robot based on the

difference of measured force and reference force This group of rules perform

similarly to classical control method

2) Force trend rule: This group of rules are specially implemented to detect the

large burs by evaluate the trend of force difference Proper set of force trend

rule could reduce overshoot of cutting force and achieves fast response

3) System failure protection rule: Used for safety purpose When speed_ratio is

already on lowest stage and process force is still high, robot will stop to avoid

motor overload and robot vibration

FLC generates change of speed_ratio through evaluating various rules Instead of changing

speed_ratio continuously as in classical PID control, speed_ratio is set to several stages The

reason behind this is that continuously adjusting feed speed is not desirable for machining

process because it increase tool wear and deteriorate surface quality Since a too slow feed

speed will change the chip generation mechanism, that is, tool becomes rubbing instead of

cutting the workpiece; the minimal feed speed is also set Although ideally more stages

means more control accuracy, five stages (0.2, 0.4, 0.6 0.8, 1.0) would be enough for most

applications A special case is two-stage switching control which has only low or full speed

Two-stage switching control, which sacrifices control accuracy to achieve faster response, is

a very attractive control method for many deburring process One such example will be

presented in the next session

4.4 Experimental Results for CMRR

Experimental studies are conducted for an end milling process to verify the stability and

performance of the proposed PI control and adaptive control algorithm The robot used in

the milling process is the ABB IRB 6400, the same robot on which we have done the

parameter identification The setup of robotic end milling process is shown as Fig 6

During the end milling experiment, a spindle was hold by the robot arm, and an aluminum

block (AL2040) is fixed on a steel table The cutting depth of the process was changed from 1

mm to 3 mm with a step of 1 mm Both fixed gain PI control algorithm and self-tuning PI

control algorithm, proposed, were tested with the same experimental setup The control

system performance and stability are compared for these two controllers The experiment

results for fixed-gain PI controller and for self-tuning PI controller are shown in Fig 11 and

Fig 12, respectively

The reference force was set at 250 N for the experiments When the cutting depth is 1mm,

both controllers are saturated with a full command speed at 30 mm/s When the cutting

depth changed to 2 mm, the fixed-gain PI controller started to vibrate, but still stable When

the cutting depth changed to 3 mm, the fixed-gain PI controller became unstable, just as

predicted in the simulation results On the other hand, the self-tuning adaptive controller

maintained the stability and performance for all the cutting depths

0100200300

Fig 11 Fixed-gain PI control experiment result

0100200300

to remove the burs The limit of this system is the spindle power, which is equivalent to about 300 N Without the CMRR function, the spindle will stall at the bur location and the entire system setup will be damaged Since the bur location and size are not predicable,

normally the command feed speed is set to be a very conservative value, such as 30~40

mm/s With FLC MRR control, command feed speed is set to 100ms Two-stage switch

control (0.5, 1.0) is sufficient to keep the system under spindle limit The motor current

signal (blue) is also recorded for comparison purpose It could be shown that after a linear

conversion (a gain and an offset), spindle current is equivalent to machining force signal

Either signal could be used for feedback here Note that the force measurements in the

experiments were filtered with a low-pass filter before used (Fig 13)

Fig 13 FLC MRR control result

5 Robot Deformation Compensation

Among the many sources of errors of machine tools, thermal deformation and geometric

errors are traditionally known as key contributors For example, by studying a large amount

of data, (Bryan, 1990) reported that thermal errors could contribute as much as 70% of

workpiece errors in precision machining RTEC techniques for geometric and thermal errors

have successfully improved machine tool accuracy up to one order of magnitude (Donmez,

1986) (Chen, 1993)

After the geometric and thermal errors are compensated for, cutting force induced errors

become the major source of machine tool errors (Bajpai, 1972) and (Kops, et al., 1994)

attempted to overcome the errors due to deflection using the relationship between

workpiece deflection and the depth-of-cut applied at the final pass However, most of the

current error compensation research has not considered the cutting force induced errors

The following argument has been used to justify the neglect of the cutting force induced

errors: in finish machining, the cutting force is small and the resulting deflection can be

neglected

However, in robotic machining process, due to the low stiffness of the industrial robot, the

force induced deformation of the robot structure is the single most dominant source of

workpiece surface error Offline calibration strategies are often used to improve accuracy

while sacrificing operation cycle time The workpiece is calibrated with a distance sensor,

usually LVDT or laser sensor before and after the machining process The surface error is measured and calculated to update the tool/workpiece data of the next cut Although offline calibration could improve robot path error as well as force induced error, the process cycle time is increased, mostly doubled With force sensor attached on the robot wrist, force information is ready on real time If an accurate stiffness model could be established, the force induced error could be compensated online by updating the robot targets

5.1 Robot Stiffness Modeling

A robot stiffness model, which relates the force applied on the robot tool end point to the deformation of the tool end point in Cartesian space, is crucial for robot deformation compensation, since the force measurement and control is fulfilled in Cartesian space while the robot position control is implemented in joint space

The proposed model must be accurate enough for a great improvement of the surface error,

as well as simple enough for real-time implementation Detailed modelling of all the mechanical components and connections will bring a too complicated model for real-time control; and difficulties for accurate parameter identification

The sources of the stiffness of a typical robot manipulator are the compliance of its joints, actuators and other transmission elements, geometric and material properties of the links, base, and the active stiffness provided by its position control system (Alici & Shirinzadeh, 2005) As commercial robotic systems are designed to achieve high positioning accuracy, elastic properties of the arms are insignificant The dominant influence on a large deflection

of the manipulator tip position is joint compliance, e.g., due to reducer elasticity (Pan et al., 2006)

The conventional formulation for the mapping of stiffness matrices between the joint and Cartesian spaces, was first derived by (Salisbury, 1980) and generally has been accepted and applied

1) ( )

 J Q K J Q

x (16) Where Kq is a 6×6 diagonal joint stiffness matrix, which relates the motor torque load  on six joints to the 6×1 joint deformation vector Q,

Q



 (17) )

F  x  (18)

Eq (16) can be derived from the definition of Jacobian matrix in Eq (19) and the principle of virtual work in Eq (20)

Q Q J

 ( ) (19)

normally the command feed speed is set to be a very conservative value, such as 30~40

mm/s With FLC MRR control, command feed speed is set to 100ms Two-stage switch

control (0.5, 1.0) is sufficient to keep the system under spindle limit The motor current

signal (blue) is also recorded for comparison purpose It could be shown that after a linear

conversion (a gain and an offset), spindle current is equivalent to machining force signal

Either signal could be used for feedback here Note that the force measurements in the

experiments were filtered with a low-pass filter before used (Fig 13)

Fig 13 FLC MRR control result

5 Robot Deformation Compensation

Among the many sources of errors of machine tools, thermal deformation and geometric

errors are traditionally known as key contributors For example, by studying a large amount

of data, (Bryan, 1990) reported that thermal errors could contribute as much as 70% of

workpiece errors in precision machining RTEC techniques for geometric and thermal errors

have successfully improved machine tool accuracy up to one order of magnitude (Donmez,

1986) (Chen, 1993)

After the geometric and thermal errors are compensated for, cutting force induced errors

become the major source of machine tool errors (Bajpai, 1972) and (Kops, et al., 1994)

attempted to overcome the errors due to deflection using the relationship between

workpiece deflection and the depth-of-cut applied at the final pass However, most of the

current error compensation research has not considered the cutting force induced errors

The following argument has been used to justify the neglect of the cutting force induced

errors: in finish machining, the cutting force is small and the resulting deflection can be

neglected

However, in robotic machining process, due to the low stiffness of the industrial robot, the

force induced deformation of the robot structure is the single most dominant source of

workpiece surface error Offline calibration strategies are often used to improve accuracy

while sacrificing operation cycle time The workpiece is calibrated with a distance sensor,

usually LVDT or laser sensor before and after the machining process The surface error is measured and calculated to update the tool/workpiece data of the next cut Although offline calibration could improve robot path error as well as force induced error, the process cycle time is increased, mostly doubled With force sensor attached on the robot wrist, force information is ready on real time If an accurate stiffness model could be established, the force induced error could be compensated online by updating the robot targets

5.1 Robot Stiffness Modeling

A robot stiffness model, which relates the force applied on the robot tool end point to the deformation of the tool end point in Cartesian space, is crucial for robot deformation compensation, since the force measurement and control is fulfilled in Cartesian space while the robot position control is implemented in joint space

The proposed model must be accurate enough for a great improvement of the surface error,

as well as simple enough for real-time implementation Detailed modelling of all the mechanical components and connections will bring a too complicated model for real-time control; and difficulties for accurate parameter identification

The sources of the stiffness of a typical robot manipulator are the compliance of its joints, actuators and other transmission elements, geometric and material properties of the links, base, and the active stiffness provided by its position control system (Alici & Shirinzadeh, 2005) As commercial robotic systems are designed to achieve high positioning accuracy, elastic properties of the arms are insignificant The dominant influence on a large deflection

of the manipulator tip position is joint compliance, e.g., due to reducer elasticity (Pan et al., 2006)

The conventional formulation for the mapping of stiffness matrices between the joint and Cartesian spaces, was first derived by (Salisbury, 1980) and generally has been accepted and applied

1) ( )

 J Q K J Q

x (16) Where Kq is a 6×6 diagonal joint stiffness matrix, which relates the motor torque load  on six joints to the 6×1 joint deformation vector Q,

Q



 (17) )

F  x  (18)

Eq (16) can be derived from the definition of Jacobian matrix in Eq (19) and the principle of virtual work in Eq (20)

Q Q J

 ( ) (19)

Q X

FT    T   (20) For articulated robot, Kx is not a diagonal matrix and it is configuration dependent This

means: first, the force and deformation in Cartesian space is coupled, the force applied in

one direction will cause the deformation in all directions; second, at different positions, the

stiffness matrix will take different values

(Chen & Kao, 2000) introduced a more complex model using a new conservative

congruence transformation as the generalized relationship between the joint and Cartesian

stiffness matrices in order to preserve the fundamental properties of the stiffness matrices

1) ( ) (

Kg T( ) (22)

where Kg is a 6×6 matrix defining the changes in geometry via the differential Jacobian; F

is external applied force

The second model is more difficult to implement as the differential Jacobian is not available

in the robot controller The difference between these two models is the additional Kg in the

second model Kg accounts for the change in geometry under the presence of external load

IRB6400, a typical large sized industrial robot has a payload of 150kg, which will cause

about 3 mm deformation considering its stiffness is around 0.5N/μm From our calculation,

g

K is negligible compared to Kq as this is a relative small deformation compared to the

scale of robot structure

Thus, the conventional formulation is selected in this research for stiffness modelling In this

model, robot stiffness is simplified to six rotational stiffness coefficients, that is, equivalent

torsional spring with stiffness K as each joint is actuated directly with AC motor Also from

the control point of view, this model is the easiest to implement, since these are the 6 degree

of freedom of the robot, which could be directly compensated by joint angles Since the axis

of force sensor is coincide with the axis of joint six, the stiffness of force sensor and its

connection flange could be modelled into joint six

5.2 Parameter Identification of the Stiffness Model

Experimental identification of the robot stiffness model parameters, joint stiffness of six

joints, is critical in fulfilling real-time position compensation In our model, the joint stiffness

is an overall effect contributed by motor, joint link, and gear reduction units It is not

realistic and accurate to identify the stiffness parameter of each joint directly by dissembling

the robot as the assembly process will affect the stiffness of the robot arm The practical

method is to measure it in Cartesian space

The setup of robot stiffness measurement is shown in Fig 14 The cutting tool at the effector is replaced by a sphere-tip When robot is driven to a fixed position in the workspace, the joint angles of the robot are recorded A weight is applied on the tool tip to generate a deformation The position of the sphere-tip is measured by ROMOR CMM machine before and after the weight is applied to and the 3-DOF translational deformation

end-is calculated The applied force end-is measured by 6 DOF ATI force/torque sensor A pulley end-is used to generate force on other directions than vertical down direction

Fig 14 Methodology of robot stiffness measurement Given the kinematic parameters of the robot, the Jacobian matrix at any robot position could

be calculated using robotics toolbox for MATLAB Table 1 shows the IRB6400 kinematic model in Denavit-Hartenberg parameters

The same procedure is repeated at multiple positions in the robot workspace and with different loads From the relationship of

X Q J K Q J

F  ( )T q ( ) 1  (23)

q

K could be solved by least square method, givenF,J (Q ) and  X Only the first three equations from Eq (23) are used in calculation as the orientation and torque are hard to measure accurately in the setup The calibration results show that the standard deviation of the stiffness data is small, which means constant model parameter is adequate to model the deformation of robot The deviation in the entire work space is less than 0.04mm

Q X

FT    T   (20) For articulated robot, Kx is not a diagonal matrix and it is configuration dependent This

means: first, the force and deformation in Cartesian space is coupled, the force applied in

one direction will cause the deformation in all directions; second, at different positions, the

stiffness matrix will take different values

(Chen & Kao, 2000) introduced a more complex model using a new conservative

congruence transformation as the generalized relationship between the joint and Cartesian

stiffness matrices in order to preserve the fundamental properties of the stiffness matrices

1)

( )

( )

x (21) With

Kg T( ) (22)

where Kg is a 6×6 matrix defining the changes in geometry via the differential Jacobian; F

is external applied force

The second model is more difficult to implement as the differential Jacobian is not available

in the robot controller The difference between these two models is the additional Kg in the

second model Kg accounts for the change in geometry under the presence of external load

IRB6400, a typical large sized industrial robot has a payload of 150kg, which will cause

about 3 mm deformation considering its stiffness is around 0.5N/μm From our calculation,

g

K is negligible compared to Kq as this is a relative small deformation compared to the

scale of robot structure

Thus, the conventional formulation is selected in this research for stiffness modelling In this

model, robot stiffness is simplified to six rotational stiffness coefficients, that is, equivalent

torsional spring with stiffness K as each joint is actuated directly with AC motor Also from

the control point of view, this model is the easiest to implement, since these are the 6 degree

of freedom of the robot, which could be directly compensated by joint angles Since the axis

of force sensor is coincide with the axis of joint six, the stiffness of force sensor and its

connection flange could be modelled into joint six

5.2 Parameter Identification of the Stiffness Model

Experimental identification of the robot stiffness model parameters, joint stiffness of six

joints, is critical in fulfilling real-time position compensation In our model, the joint stiffness

is an overall effect contributed by motor, joint link, and gear reduction units It is not

realistic and accurate to identify the stiffness parameter of each joint directly by dissembling

the robot as the assembly process will affect the stiffness of the robot arm The practical

method is to measure it in Cartesian space

The setup of robot stiffness measurement is shown in Fig 14 The cutting tool at the effector is replaced by a sphere-tip When robot is driven to a fixed position in the workspace, the joint angles of the robot are recorded A weight is applied on the tool tip to generate a deformation The position of the sphere-tip is measured by ROMOR CMM machine before and after the weight is applied to and the 3-DOF translational deformation

end-is calculated The applied force end-is measured by 6 DOF ATI force/torque sensor A pulley end-is used to generate force on other directions than vertical down direction

Fig 14 Methodology of robot stiffness measurement Given the kinematic parameters of the robot, the Jacobian matrix at any robot position could

be calculated using robotics toolbox for MATLAB Table 1 shows the IRB6400 kinematic model in Denavit-Hartenberg parameters

The same procedure is repeated at multiple positions in the robot workspace and with different loads From the relationship of

X Q J K Q J

F  ( )T q ( ) 1  (23)

q

K could be solved by least square method, givenF,J (Q ) and  X Only the first three equations from Eq (23) are used in calculation as the orientation and torque are hard to measure accurately in the setup The calibration results show that the standard deviation of the stiffness data is small, which means constant model parameter is adequate to model the deformation of robot The deviation in the entire work space is less than 0.04mm

Table 1 DH model of IRB 6400

5.3 Real-time robot deformation compensation

The major sources of position error in robotic machining process can be classified into two

classes, 1) machining force oriented error, and 2) motion error (kinematic, measurement and

servo errors, etc.) The motion error is inherent from robot position controller and will

appear even in non-contact movement While the machining force in the milling process will

typically over several hundreds of Newton, the force oriented error, which will easily go up

to 0.5mm, is the dominant factor of surface error Our objective here is to measure the

deformation through a viable way and compensate it online to improve the overall

machining accuracy

To our best knowledge, none of the existing research has addressed the topic of online

compensation of process force oriented robot deformation due to the lack of real-time force

information and limited access to the controller of industrial robot

Filter

s mF

old r

q

rq



Gravity Model

FrameTransform

new r

old r

q

rq



Gravity Model

FrameTransform

new r

q Robot

Controller

StiffnessModel

Fig 15 Block diagram of real-time deformation compensation

The block diagram of real time deformation compensation algorithm is shown in Fig 15

After the force sensor noise is filtrated, gravity compensation must be conducted to remove

the force reading from the weight of spindle and tool Since the robot may not always

maintain a wrist down position, a general gravity compensation algorithm is developed to

remove the gravity effects for any robot configuration The algorithm takes measurement of

gravity force at 15 distinctive robot configurations and uses least square method to calculate

the mass and center of mass coordinates This information is then updated to the robot tool

data and the robot will always offset the gravity from the force reading at any robot

configurations

The force signal read from the sensor frame is then translated into the robot tool frame

Based on the stiffness model identified before, the deformation due to machining force is

calculated online and the joint reference for robot controller is updated accordingly

5.4 Experimental Results

The experimental tests on both standard aluminum block and real cylinder head workpiece have been conducted to verify the results of proposed real-time deformation compensation method

5.4.1 Aluminum block end milling test

A 150mm×50mm 6063 aluminum alloy block is used for end milling test Table 2 lists the detailed parameters for the experiment

Spindle SETCO,5HP, 8000RPM Tool type SECO Φ75mm,

Square insert×6 Cutting fluid - (Dry cutting) Feed rate 20 mm/s Spindle speed 3600 RPM

Table 2 Parameters for end milling

Fig 16 Setup of aluminum end milling and surface scan

A laser distance sensor is used to measure the finished surface of aluminum block as shown

in Fig 16 The surface error without deformation compensation demonstrates anti-intuitive results, on average extra 0.4mm material was removed from the aluminum block, which is not possible for a CNC machine since the cutting force normal to the workpiece surface will always push the cutter away from the surface and cause negative surface error (cut less) The coupling of robot stiffness model explains this phenomenon When end milling using square inserts, the machining force in the robot feed direction and the cutting direction (around 300N each) are much larger than the force in the normal direction (around 50N) At this specific robot configuration, the force in feed and cutting direction will both push the cutter into the workpiece, which results in positive surface error (cut more) Since the feed force and cutting force are the major components in this setup, the overall effect is that the surface is removed 0.4 mm more than commanded depth On the other hand, the result after

Table 1 DH model of IRB 6400

5.3 Real-time robot deformation compensation

The major sources of position error in robotic machining process can be classified into two

classes, 1) machining force oriented error, and 2) motion error (kinematic, measurement and

servo errors, etc.) The motion error is inherent from robot position controller and will

appear even in non-contact movement While the machining force in the milling process will

typically over several hundreds of Newton, the force oriented error, which will easily go up

to 0.5mm, is the dominant factor of surface error Our objective here is to measure the

deformation through a viable way and compensate it online to improve the overall

machining accuracy

To our best knowledge, none of the existing research has addressed the topic of online

compensation of process force oriented robot deformation due to the lack of real-time force

information and limited access to the controller of industrial robot

Filter

s m

F

old r

q

rq



Gravity Model

FrameTransform

new r

F

old r

q

rq



Gravity Model

FrameTransform

new r

q Robot

Controller

StiffnessModel

Fig 15 Block diagram of real-time deformation compensation

The block diagram of real time deformation compensation algorithm is shown in Fig 15

After the force sensor noise is filtrated, gravity compensation must be conducted to remove

the force reading from the weight of spindle and tool Since the robot may not always

maintain a wrist down position, a general gravity compensation algorithm is developed to

remove the gravity effects for any robot configuration The algorithm takes measurement of

gravity force at 15 distinctive robot configurations and uses least square method to calculate

the mass and center of mass coordinates This information is then updated to the robot tool

data and the robot will always offset the gravity from the force reading at any robot

configurations

The force signal read from the sensor frame is then translated into the robot tool frame

Based on the stiffness model identified before, the deformation due to machining force is

calculated online and the joint reference for robot controller is updated accordingly

5.4 Experimental Results

The experimental tests on both standard aluminum block and real cylinder head workpiece have been conducted to verify the results of proposed real-time deformation compensation method

5.4.1 Aluminum block end milling test

A 150mm×50mm 6063 aluminum alloy block is used for end milling test Table 2 lists the detailed parameters for the experiment

Spindle SETCO,5HP, 8000RPM Tool type SECO Φ75mm,

Square insert×6 Cutting fluid - (Dry cutting) Feed rate 20 mm/s Spindle speed 3600 RPM

Table 2 Parameters for end milling

Fig 16 Setup of aluminum end milling and surface scan

A laser distance sensor is used to measure the finished surface of aluminum block as shown

in Fig 16 The surface error without deformation compensation demonstrates anti-intuitive results, on average extra 0.4mm material was removed from the aluminum block, which is not possible for a CNC machine since the cutting force normal to the workpiece surface will always push the cutter away from the surface and cause negative surface error (cut less) The coupling of robot stiffness model explains this phenomenon When end milling using square inserts, the machining force in the robot feed direction and the cutting direction (around 300N each) are much larger than the force in the normal direction (around 50N) At this specific robot configuration, the force in feed and cutting direction will both push the cutter into the workpiece, which results in positive surface error (cut more) Since the feed force and cutting force are the major components in this setup, the overall effect is that the surface is removed 0.4 mm more than commanded depth On the other hand, the result after

deformation compensation shows a less than 0.1 mm surface error, which is in the range of

robot path accuracy

Fig 17 A Cylinder head part, surface error of end milling in position control; B Cylinder

head part, surface error of end milling in force control

5.4.2 Cylinder Head End Milling Test

A real cylinder head workpiece is also utilized here for deformation compensation test,

using the same end milling parameters as listed in Table 2 To better visualize the surface

error, the surface is covered by orange paint after the end milling Then the tool is moved

0.1mm closer to the workpiece surface each time, until all the paint on the surface are

cleaned As shown in Fig.17A, under position control, the tool touches the surface at

-0.3mm, and clean the surface at 0.6mm, the total surface error is 0.9mm Under the force

control, the tool touches the surface at -0.1mm, and clean the surface at 0.3mm, the total

surface error reduced to 0.4mm, as shown in Fig 17B

6 Conclusion

This chapter has addressed the critical issues in robotic machining process from

programming to process control Three major contributions, including rapid robot

programming, controlled material removal rate, and online deformation compensation have

been introduced in detail The complete solution is achieved with force control strategy

based on ABB IRC5 robot controller

Rapid robot programming is characterized by two main modules: lead-through and

automatic path-learning Lead-through gives robot operator the freedom to adjust the

spatial relationship between the robot tool fixture and the workpiece easily, while robot

automatically follow the workpiece contour, record the targets and generate the process

program in path-learning Since the robot programming is generated at actual process setup,

no additional calibration is required

Online deformation compensation is realized based on a robot structure model Since force

induced deformation is the major source of inaccuracy in robotic machining process, the

surface quality is improved greatly adopting the proposed method This function is

especially important in milling applications, where cutting force could be as large as 1000 N

Regulating machining forces provides significant economic benefits by increasing operation productivity and improving part quality CMRR control the machining force by realtime adjusting the robot feed speed Various control strategy, including PID, adaptive control and fuzzy logic controller were implemented on different cutting situations

Including the chatter and vibration analysis presented in (Pan & Zhang, et al, 2006), these complete set of solutions will greatly benefit the foundry industry with small to medium batch sizes Dramatic increase of successful setups of industrial robots in foundry cleaning and pre-machining applications will be seen in the very near future

7 References

Alici, G.; Shirinzadeh, B (2005) “Enhanced Stiffness Modeling Identification and

Characterization for Robot Manipulators”, IEEE Transactions on Robotics, Vol 21,

No 4, August 2005

Donmez, M A et al (1986) “A General Methodology for Machine Tool Accuracy

Enhancement y Error Compensation”, Precision Engineering, Vol 8, No 4, pp

187-196

Bajpai, S (1972) “Optimization of Workpiece Size for Turning Accurate Cylindrical Parts”,

International Journal of Machine Tool Design and Research, Vol 12, pp 221-228

Basanez, L & Rosell, J (2005) “Robotic Polishing Systems—From graphical task

specification to automatic programming”, IEEE Robotics & Automation magazine, Sep,

2005

Bryan, J B (1990) “International Status of Thermal Error Research”, Annals of the CIRP, Vol

39, No 2, pp 645-656

Budak, E.; Altintas, Y (1998) ''Analytical Prediction of Chatter Stability Conditions for

Multi-Degree of Systems in Milling Part I: Modeling, Part II: Applications,”

Transactions of ASME, Journal of Dynamic Systems, Measurement and Control, vol.120,

pp.22-36 Chen, J S et al (1993) “Real Time Compensation of Time-variant Volumetric Error on a

Machining Center”, ASME Journal of Engineering for Industry, Vol 114, pp 472-479

Chen, S.F.; Kao, I (2000) “Conservative congruence transformation for joint and Cartesian

stiffness matrices of robotic hands and fingers”, The International Journal of Robotics

Research, Vol 19, No 9, September 2000, pp 835-847

Daneshmend, L., & Pak, H., (1986) “Model Reference Adaptive Control of Feed Force in

Turning,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol 108, No

3, pp 215-222

Galichet, S., & Foulloy, L (1995) “Fuzzy controllers: synthesis and equivalences”, IEEE

Transactions on System, Man and Cybernetics

Kim, S., Landers, R., Ulsoy, A., 2003, “Robust Machining Force Control with Process

Compensation,” Journal of Manufacturing science and engineering, Vol 125, pp

423-430 Kops, L.; Gould, M.; & Mizrach, M (1994) “A Search for Equilibrium between Workpiece

Deflection and Depth of Cut: Key to Predictive Compensation for Deflection in

Turing”, Proceedings 1994 ASME Winter Annual Meeting, Vol 68-2, pp 819-825

Landers, R & Ulsoy, A., (2000) “Model-based machining force control”, ASME Journal of

Dynamic Systems, Measurement, and Control, vol 122, no 3, 2000, pp 521-527

deformation compensation shows a less than 0.1 mm surface error, which is in the range of

robot path accuracy

Fig 17 A Cylinder head part, surface error of end milling in position control; B Cylinder

head part, surface error of end milling in force control

5.4.2 Cylinder Head End Milling Test

A real cylinder head workpiece is also utilized here for deformation compensation test,

using the same end milling parameters as listed in Table 2 To better visualize the surface

error, the surface is covered by orange paint after the end milling Then the tool is moved

0.1mm closer to the workpiece surface each time, until all the paint on the surface are

cleaned As shown in Fig.17A, under position control, the tool touches the surface at

-0.3mm, and clean the surface at 0.6mm, the total surface error is 0.9mm Under the force

control, the tool touches the surface at -0.1mm, and clean the surface at 0.3mm, the total

surface error reduced to 0.4mm, as shown in Fig 17B

6 Conclusion

This chapter has addressed the critical issues in robotic machining process from

programming to process control Three major contributions, including rapid robot

programming, controlled material removal rate, and online deformation compensation have

been introduced in detail The complete solution is achieved with force control strategy

based on ABB IRC5 robot controller

Rapid robot programming is characterized by two main modules: lead-through and

automatic path-learning Lead-through gives robot operator the freedom to adjust the

spatial relationship between the robot tool fixture and the workpiece easily, while robot

automatically follow the workpiece contour, record the targets and generate the process

program in path-learning Since the robot programming is generated at actual process setup,

no additional calibration is required

Online deformation compensation is realized based on a robot structure model Since force

induced deformation is the major source of inaccuracy in robotic machining process, the

surface quality is improved greatly adopting the proposed method This function is

especially important in milling applications, where cutting force could be as large as 1000 N

Regulating machining forces provides significant economic benefits by increasing operation productivity and improving part quality CMRR control the machining force by realtime adjusting the robot feed speed Various control strategy, including PID, adaptive control and fuzzy logic controller were implemented on different cutting situations

Including the chatter and vibration analysis presented in (Pan & Zhang, et al, 2006), these complete set of solutions will greatly benefit the foundry industry with small to medium batch sizes Dramatic increase of successful setups of industrial robots in foundry cleaning and pre-machining applications will be seen in the very near future

7 References

Alici, G.; Shirinzadeh, B (2005) “Enhanced Stiffness Modeling Identification and

Characterization for Robot Manipulators”, IEEE Transactions on Robotics, Vol 21,

No 4, August 2005

Donmez, M A et al (1986) “A General Methodology for Machine Tool Accuracy

Enhancement y Error Compensation”, Precision Engineering, Vol 8, No 4, pp

187-196

Bajpai, S (1972) “Optimization of Workpiece Size for Turning Accurate Cylindrical Parts”,

International Journal of Machine Tool Design and Research, Vol 12, pp 221-228

Basanez, L & Rosell, J (2005) “Robotic Polishing Systems—From graphical task

specification to automatic programming”, IEEE Robotics & Automation magazine, Sep,

2005

Bryan, J B (1990) “International Status of Thermal Error Research”, Annals of the CIRP, Vol

39, No 2, pp 645-656

Budak, E.; Altintas, Y (1998) ''Analytical Prediction of Chatter Stability Conditions for

Multi-Degree of Systems in Milling Part I: Modeling, Part II: Applications,”

Transactions of ASME, Journal of Dynamic Systems, Measurement and Control, vol.120,

pp.22-36 Chen, J S et al (1993) “Real Time Compensation of Time-variant Volumetric Error on a

Machining Center”, ASME Journal of Engineering for Industry, Vol 114, pp 472-479

Chen, S.F.; Kao, I (2000) “Conservative congruence transformation for joint and Cartesian

stiffness matrices of robotic hands and fingers”, The International Journal of Robotics

Research, Vol 19, No 9, September 2000, pp 835-847

Daneshmend, L., & Pak, H., (1986) “Model Reference Adaptive Control of Feed Force in

Turning,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol 108, No

3, pp 215-222

Galichet, S., & Foulloy, L (1995) “Fuzzy controllers: synthesis and equivalences”, IEEE

Transactions on System, Man and Cybernetics

Kim, S., Landers, R., Ulsoy, A., 2003, “Robust Machining Force Control with Process

Compensation,” Journal of Manufacturing science and engineering, Vol 125, pp

423-430 Kops, L.; Gould, M.; & Mizrach, M (1994) “A Search for Equilibrium between Workpiece

Deflection and Depth of Cut: Key to Predictive Compensation for Deflection in

Turing”, Proceedings 1994 ASME Winter Annual Meeting, Vol 68-2, pp 819-825

Landers, R & Ulsoy, A., (2000) “Model-based machining force control”, ASME Journal of

Dynamic Systems, Measurement, and Control, vol 122, no 3, 2000, pp 521-527